A related quantity that is also of great interest is the Fubini-Study complexity (FSC) [1]}, [2]}.
Contrary to the NC, this quantification arises from the quantum information metric (QIM)
[3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}, which is
the real part of a more generic structure called the quantum geometric tensor, whose imaginary part
gives the Berry phase. The QIM being the Riemannian metric induced on the parameter space of the Hamiltonian (which
will always be two dimensional in our case), measures the distance between two neighbouring quantum states. The FSC
is then the geodesic distance on the parameter manifold. Specifically, given a wave function \(\mathinner {|{\Psi }\rangle }\) , the
geometric tensor reads
\(\chi _{ij}=\mathinner {\langle {\partial _{i}\Psi }|}\partial _{j}\Psi \rangle -\mathinner {\langle {\partial _{i}\Psi }|}\Psi \rangle \mathinner {\langle {\Psi }|}\partial _{j}\Psi \rangle ~,\) 
